Linear vs Nonlinear Systems

Linear Systems

A system is linear if:

• Output is proportional to input
• Superposition principle holds

Example:

$$ m\ddot{x} + kx = 0 $$

Nonlinear Systems

A system is nonlinear if:

• Equations contain nonlinear terms
• Superposition does not apply

Example:

$$ \ddot{x} + x^3 = 0 $$